Final answer:
The question requires calculating the proper serving angle in tennis using the principles of projectile motion, given the initial serving speed, height of the serve, the height of the net, and the distance to the service box. To determine the correct angle, the tennis serve is modeled mathematically as a physics problem involving kinematic equations.
Step-by-step explanation:
We are tasked with calculating the angle at which a tennis player must serve a ball so that it just crosses the net and determining if it will land in the service box. The player serves at a speed of 170 km/h (which is approximately 47.22 m/s), from a height of 2.5 m, the net is 0.91 m high, and the distance from the baseline to the net is 11.9 m.
First, we convert the speed from km/h to m/s. Then, using the kinematic equations and the information provided, we aim to find at which angle θ the ball should be served so it barely clears the height of the net. This involves calculating the ball's trajectory and ensuring the required conditions for both net clearance and landing within the service box.
To find the angle, we need to solve a problem involving projectile motion, where we need to ensure that the vertical position of the ball is just above 0.91 m when it crosses the net. Furthermore, we need to check if the ball will land within the service box, which requires the horizontal distance traveled by the ball to be less than 6.40 m from the net when it lands.
Given the complexity of the calculations, which involve both trigonometry and physics, we need to use the appropriate projectile motion equations with known variables such as initial velocity, distance, height, and gravitational acceleration.